Skip to main content
SpringerLink
Log in

Complete geometric nonlinear formulation for rigid-flexible coupling dynamics

  • Published:
Journal of Central South University of Technology Aims and scope Submit manuscript

Abstract

A complete geometric nonlinear formulation for rigid-flexible coupling dynamics of a flexible beam undergoing large overall motion was proposed based on virtual work principle, in which all the high-order terms related to coupling deformation were included in dynamic equations. Simulation examples of the flexible beam with prescribed rotation and free rotation were investigated. Numerical results show that the use of the first-order approximation coupling (FOAC) model may lead to a significant error when the flexible beam experiences large deformation or large deformation velocity. However, the correct solutions can always be obtained by using the present complete model. The difference in essence between this model and the FOAC model is revealed. These coupling high-order terms, which are ignored in FOAC model, have a remarkable effect on the dynamic behavior of the flexible body. Therefore, these terms should be included for the rigid-flexible dynamic modeling and analysis of flexible body undergoing motions with high speed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. HONG Jia-zhen. Computational dynamics of multibody system [M]. Beijing: High Education Press, 1999. (in Chinese)

    Google Scholar 

  2. TANG Hua-ping, TANG Chun-xi, YIN Chen-feng. Optimization of actuator/sensor position of multi-body system with quick startup and brake [J]. Journal of Central South University of Technology, 2007, 14(6): 803–807.

    Article  MathSciNet  Google Scholar 

  3. KANE T, RYAN R. BANERJEE A. Dynamics of a cantilever beam attached to a moving base [J]. Journal of Guidance, Control and Dynamics, 1987, 10: 139–151.

    Article  Google Scholar 

  4. MAYO J, DOMINGUEZ J. Finite element geometrically nonlinear dynamic formulation of flexible multibody systems using a new displacements representation [J]. Journal of Vibration and Acoustics, 1997, 119: 573–581.

    Article  Google Scholar 

  5. YOO H H, CHUNG J, CHUANG J. Equilibrium and modal analyses of rotating multibeam structures employing multiple reference frames [J]. Journal of Sound and Vibration, 2007, 302: 789–805.

    Article  Google Scholar 

  6. LIA A Q, LIEW K M. Non-linear substructures approach for dynamic analysis of rigid-flexible multibody system [J]. Computer Methods in Applied Mechanics and Engineering, 1994, 114: 379–396.

    Article  Google Scholar 

  7. SHABANA A A, MIKKOLA A M. Use of the finite element absolute nodal coordinate formulation in modeling slop discontinuity [J]. Trans ASME J Mech Des, 2003, 125: 342–350.

    Article  Google Scholar 

  8. SUGIYAMA H, GERSTMAY S, SHABANA A A, Deformation modes in the finite element absolute nodal coordinate formulation [J]. Journal of Sound and Vibration, 2006, 298: 1129–1149.

    Article  MathSciNet  Google Scholar 

  9. JIANG Li-zhong, HONG Jia-zhen. Coupling dynamics of the elastic beam with translation [J]. Chinese Quarterly of Mechanics, 2002, 23(4): 450–454. (in Chinese)

    Google Scholar 

  10. LIU Jin-yang. Study of dynamic modeling theory of rigid-flexible coupling system [D]. Shanghai: Department of Engineering Mechanics, Shanghai Jiao Tong University, 2000. (in Chinese)

    Google Scholar 

  11. YANG Hui, HONG Jia-zhen, YU Zheng-yue. Dynamics modeling of a flexible hub-beam system with a tip mass [J]. Journal of Sound and Vibration, 2003, 266(4): 759–774.

    Article  Google Scholar 

  12. LIU Jin-yang, HONG Jia-zhen. Geometric stiffening effect on rigid-flexible coupling dynamics of an elastic beam [J]. Journal of Sound and Vibration, 2004, 278(4/5): 1147–1162.

    Article  Google Scholar 

  13. CAI G P, LIM C W. Optimal tracking control of a flexible hub-beam system with time delay [J]. Multibody System Dynamics, 2006, 16: 331–350.

    Article  MATH  Google Scholar 

  14. DONG Xing-jian, MENG Guang, CAI Guo-ping. Dynamic modeling and analysis of a rotating flexible beam [J]. Journal of Vibration Engineering, 2006, 19(4): 488–493. (in Chinese)

    Google Scholar 

  15. HUANG You-an, DENG Zi-chen, YAO Lin-xiao. Dynamic analyze of a rotating rigid-flexible coupled smart structure with large deformation [J]. Applied Mathematics and Mechanics, 2007, 28(10): 1203–1212.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai, 200240, China

    Zhu-yong Liu  (刘铸永), Jia-zhen Hong  (洪嘉振) & Jin-yang Liu  (刘锦阳)

Authors
  1. Zhu-yong Liu  (刘铸永)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jia-zhen Hong  (洪嘉振)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jin-yang Liu  (刘锦阳)
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhu-yong Liu  (刘铸永).

Additional information

Foundation item: Project(10772113) supported by the National Natural Science Foundation of China

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, Zy., Hong, Jz. & Liu, Jy. Complete geometric nonlinear formulation for rigid-flexible coupling dynamics. J. Cent. South Univ. Technol. 16, 119–124 (2009). https://doi.org/10.1007/s11771-009-0020-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11771-009-0020-8

Key words

Search

Navigation